DSM 6.1.4-15217 Update 2 on a DS713+.
Yeah I couldn’t find any other references to this particular problem, but since it was a little non-obvious I thought it worth mentioning in case anyone else encountered it. I don’t think I’ve done anything particularly weird on my machine, or misconfigured or broken it in any obvious way, but that was what happened when I installed it.
The file permission issues I mentioned turned out to be a result of “the infamous Mono certificates issue”.